I agree with your cautionary stance on stereotypes, but the difference between men and women is a little like the overlapping wave formations on a graph, if you know what I’m trying to say. As a general rule, men will look at things in a factual way and focus on how to get things done. Women (myself included) have more of a tendency to focus on how things make us feel, as well as taking facts into account. This does not mean that men don’t feel or that all women are overly emotional.
More women are in positions of power now. I’m sure that some of them are great at it, but clearly, we are not functioning as well as we used to. (I’m 75, so I notice the difference.)